Timeline for "Misbehaved" differential equations
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2010 at 14:28 | comment | added | kakaz | Probably the granular media are best physical example of systems which do not allows easily description by differential continuous models is disputable: en.wikipedia.org/wiki/Contact_dynamics In multi body regime of contact dynamics, where You consider for example sand, there is serious problem to obtain phenomenological equations from microscopic one. Microscopic system is too overcomplicated and we believe there should be simpler macroscopic PDE. But such systems dynamic is very complicated and we have troubles to model it on the macroscopic level. | |
| Feb 4, 2010 at 19:10 | history | edited | Steve Huntsman |
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| Oct 29, 2009 at 20:01 | vote | accept | vonjd | ||
| Oct 29, 2009 at 19:56 | answer | added | j.c. | timeline score: 2 | |
| Oct 29, 2009 at 19:19 | answer | added | S. Carnahan♦ | timeline score: 2 | |
| Oct 29, 2009 at 19:00 | comment | added | vonjd | But in a sense that is what you do (at least in my opinion) when you approximate continous problems with discrete ansätze, e.g. numerical solution of differential equation with difference equations. So you take one metric and approximate it with another by letting the mesh getting finer and finer -> hoping that the discrete measure converges to the continous - which works fine in most settings, but not here! | |
| Oct 29, 2009 at 18:54 | comment | added | Qiaochu Yuan | All that means is that length isn't a continuous function in whatever topology you're imposing on curves. I don't see what this has to do with differential equations. | |
| Oct 29, 2009 at 18:49 | comment | added | j.c. | But it shouldn't move to Sqrt(2), that's the distance in the Euclidean metric, and you're talking about distances under the taxicab metric... | |
| Oct 29, 2009 at 18:46 | history | edited | vonjd | CC BY-SA 2.5 |
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| Oct 29, 2009 at 18:45 | comment | added | vonjd | What I mean is that when you try to evaluate a length in a continous setting by a discrete approximation. It simply stays at 2 and doesn't move towards Sqrt(2). | |
| Oct 29, 2009 at 18:33 | comment | added | j.c. | increasingly finer subdivisions, I mean | |
| Oct 29, 2009 at 18:33 | comment | added | j.c. | I don't understand your first paragraph - as you say, the length of the diagonal curve of a square is 2 in the taxicab metric. So why would you say that "the solution doesn't converge". The sum of distances of subdivisions of the diagonal certainly converges to 2 in the taxicab metric. | |
| Oct 29, 2009 at 18:25 | history | asked | vonjd | CC BY-SA 2.5 |